BIZOMAT MAKEOS · Gears
Spur and Helical Gear Contact (Pitting) Stress
What contact stress does this gear mesh run at, compared with the allowable for the material?
Nominal contact (Hertzian) stress at the pitch point of a spur or helical gear pair by the ISO 6336-style relation with elasticity and zone factors, as a screening check against pitting.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tangential force | N | Tangential force at the pitch circle (see the gear tooth forces tool). |
| Pinion pitch diameter | mm | Pitch diameter of the pinion. |
| Face width | mm | Face width in contact. |
| Gear ratio (gear ÷ pinion teeth) | Tooth ratio; use it as negative for internal gears is not supported here. | |
| Pressure angle | ° | Pressure angle. |
| Elastic modulus (both gears) | GPa | Modulus of the gear material. |
| Poisson’s ratio | Poisson’s ratio. | |
| Load factor (application × dynamic × distribution) | Product of application, dynamic and load-distribution factors from your rating method. | |
| Allowable contact stress | MPa | Allowable contact stress for the material and heat treatment (e.g. from ISO 6336-5 or AGMA data). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Tangential force
- What it is
- The force pushing on the gear teeth tangent to the pitch circle: torque divided by pitch radius. The gear tooth forces tool can supply it.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Contact stress rises with the square root of the force.
- Get it right
- Use the nominal force here; application and dynamic effects go in the load factor.
What this means: Pinion pitch diameter
- What it is
- The pitch diameter of the smaller gear (the pinion): module times tooth count for a spur gear.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Contact stress falls with the square root of the pinion diameter.
- Get it right
- Use the pitch diameter, not the outside (tip) diameter.
What this means: Face width
- What it is
- The width of the teeth in contact, measured along the gear axis, using the narrower gear if the two differ.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Contact stress falls with the square root of the face width.
- Get it right
- Use the face width that actually meshes, not the wider blank of one gear.
What this means: Gear ratio (gear ÷ pinion teeth)
- What it is
- The number of teeth on the larger gear divided by the number on the pinion, which is always one or more.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 100. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Divide gear teeth by pinion teeth, not the other way round. Internal gears are not handled by this tool.
What this means: Pressure angle
- What it is
- The pressure angle of the gear teeth, the angle of the line of action from the tangent to the pitch circle, as specified on the gear drawing.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For helical gears, use the transverse pressure angle consistent with your rating method.
What this means: Elastic modulus (both gears)
- What it is
- The Young’s modulus of the gear material, assumed the same for both gears, from the material data sheet.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 206 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter gigapascals: 1 GPa = 1000 MPa.
What this means: Poisson’s ratio
- What it is
- Poisson’s ratio of the gear material, assumed the same for both gears, from the material data sheet.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 0.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It is a pure ratio, not a percentage.
What this means: Load factor (application × dynamic × distributi…
- What it is
- The product of the application, dynamic and face-load distribution factors from your gear rating method, which raises the nominal load to allow for shock, speed and misalignment.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Contact stress rises with the square root of the load factor.
- Get it right
- Multiply the individual factors together before entering them.
What this means: Allowable contact stress
- What it is
- The contact stress the gear material and heat treatment can take without pitting, from rating data such as ISO 6336-5 or AGMA, used for the pass or fail check.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the allowable contact stress for the actual hardness and quality grade; it is not the tensile strength.
Method and formulas
- Elasticity factor ZE = √(E ÷ 2π(1 − ν²)) for equal materials (≈ 189.8 √MPa for steel).
- Zone factor ZH = √(2 ÷ (sin α cos α)) for unshifted spur gears (≈ 2.49 at 20°).
- σH = ZE ZH √(K Ft (u + 1) ÷ (b d₁ u)).
- Example: 3000 N on a 60 mm pinion, 30 mm wide, ratio 3: σH ≈ 864.49 MPa.
Limitations
- Screening relation; a full ISO 6336 or AGMA 2001 rating adds contact ratio, helix, lubrication and life factors.
- Same material for both gears.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Screen gear face width and diameter for pitting
- Compare materials and heat treatments
- Check a gear set after a power increase
Who it is for
- Gear designers
- Design engineers
What you get
- Elasticity and zone factors
- Contact stress
- Ratio to allowable
Interpreting the result
- Contact stress falls with the square root of face width and pinion diameter; doubling width cuts stress by about 30%.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2160, 2301–2309. Topic reference; no source tables or recommended settings are reproduced.
- ISO 6336-2 Calculation of load capacity of spur and helical gears — Surface durability (pitting)
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Open the Spur and Helical Gear Contact (Pitting) Stress calculator